Attempting to trisect an angle using an unmarked ruler and compass has been a long-standing problem of considerable interest. Reference may be made to the text of C. Stanley Ogilvy, "Excursions In Geometry", pages 135-141, wherein this is referred to as one of "The Unsolved Problems Of Antiquity"; and to the text of Leslie Miller, "College Geometry", pages 193-197, wherein this is referred to as "Impossible Ruler and Compass Constructions".
It is possible, however, to provide geometric instruments that will trisect angles. In my prior U.S. Pat. No. 3,224,097 there is illustrated a geometric instrument which can be used for providing an indication of an angle which is one-third of a given angle, i.e. trisected, or in the alternative for providing an indication of an angle which is three times a given angle, i.e. triplicated.
In my aforementioned patented geometric instrument, there is provided a base with three pivotally connected members on the base. In particular, there is included a base having a slot extending in a straight path. A guide member has one end secured within the slot and is adapted for rotational and longitudinal movement about the slot. The guide member has an elongated slot extending inwardly from its outer free end toward a point of sliding connection with the base member slot. A pair of equal length link members each have one end pivotally connected to the base member at a common point for pivoting relative thereto. One of the link members is pivotally connected to the guide member at a point on the guide member inwardly of the slot and spaced from the point of pivotal connection to the guide member within the slot by a distance which corresponds to the length of the first link to the guide member.
The second link member has its outer end connected for slidable movement within the slot of the guide member. An angle indicating scale extends outwardly from the end of each of the link members for indicating the instantaneous angular position thereof relative to a reference line extending through the length of the slot in the base member and the point of pivotal connection of the links. Accordingly, with rotation of the links, one end of one link slides within the slotted portion of a guide means and simultaneously the slidable connection of the guide means moves within the slot. The pointer associated with one link indicates an angular position relative to the path of the base slot which is three times the angle indicated by the angle scale indicator.
Following the issuance of my '097 patent, several other patents of others have issued illustrating angle dividing and trisecting devices. Reference may be made for instance to the following U.S. Pat. Nos. of interest: 3,693,261; 3,906,638; 3,919,777; 4,545,130; 4,866,848.
All of the aforementioned patents contain several components all of which must be manufactured and then assembled into the composite instrument. For instance, in my '097 patent, there is included a base plate with slots, a guide member with a slot, and two link members all of which must be assembled as described in the patent to provide reliable trisection of an angle.
It is now desired to provide a precise geometric instrument for trisecting angles which has less components and is easier to manufacture and assemble. It is also desired to manufacture an improved geometric instrument for trisecting angles which is less expensive to manufacture and easier to operate than any of the presently known devices, while at the same time providing a precise angle trisecting and angle triplicating indication.